Faculty of Physics
M.V.Lomonosov Moscow State University
Theoretical and mathematical physics

## The application of the theory of contrast structures for describing wind field in spatially heterogeneous vegetation cover.

### N.T. Levashova$^1$, J.V. Muhartova$^1$, M.A. Davydova$^1$, N.E. Shapkina$^1$, A.V. Oltchev$^2$

Moscow University Physics Bulletin 2015. 70. N 3. P. 167

The twodimensional mathematical model based on the theory of contrast structures is proposed for solving the problem of the wind flow over some obstacles in the form of shelterbelt. With the help of numerical calculations the wind fields around the shelterbelts of different spatial sizes and vertical structures are obtained.

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## Sublattices in crystals based on Wyckoff sets

### A.S. Poplavnoi

Moscow University Physics Bulletin 2015. 70. N 3. P. 175

Space groups were found where structural sublattices that are based on Wyckoff sets occur. The data about the compatibility of Delaunay types for lattices and sublattices are presented in detail for tetragonal system crystals, the structures of 19843 crystals are analyzed from a database for inorganic crystalline structures, and some examples are given. The results can be applied when studying the structures of complex crystalline compounds to find additional latent symmetry and predict the peculiarities of physical and phys icalchemical properties due to this latent symmetry.

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## $H^{+}_{2}$ in a lattice of cavities: ammonia-like splitting of the lowest level

### K.A. Sveshnikov, A.V. Tolokonnikov

Moscow University Physics Bulletin 2015. 70. N 3. P. 181

It is shown that reconstruction of the lowlying energy levels of the $H^{+}_{2}$ ion under conditions of confinement in a given spatial volume is substantially more significant as compared to the confinement by simple potential barrier. Depending on the cavity parameters, the ground-state binding energy of $H^{+}_{2}$ could be significantly greater than that of the free ion, while the behavior of the lowest molecular term $^{2}\Sigma^{+}_{g}$ of the ion turns out to be quite different when considered as a function of the internuclear distance. In particular, two minima might occur in $^{2}\Sigma^{+}_{g}$, while the relationship between them could be sufficiently different depend ing on the cavity parameters, which is shown on the phase diagram that was obtained in the work. We studied the case of a <<mexican hat>> structure of the effective ion potential in detail. As a result, the lowest electronic level of ion splits into the ground state level and the first excited one, with difference between them being as small as ~10$^{–4}$ eV. As in the NH$_3$ molecule, in the last case the lowest level gives rise to an effective two-level system that is separated from the vibrational and rotational modes by a wide energy gap. More concretely, calculation using the Neumann conditions that actually reproduce the confinement on a lattice of similar cavities shows that the splitting of ~10$^{–4}$ eV occurs for the linear sizes of the confinement area of the order of some $a_{B}$ and a shell potential magnitude of ~10 eV.

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Physics of nuclei and elementary particles

## The industrial iDREAM detector for neutrino monitoring of the operating modes of nuclear reactors

### M.B. Gromov$^1$, G.A. Lukjanchenko$^2$, D.S. Markov$^2$, G.J. Novikova$^3$, B.A. Obinyakov$^2$, A.Y. Oralbayev$^2$, M.D. Skorohvatov$^2$, S.V. Sukhotin$^2$, A.S. Chepurnov$^4$, A.V. Etenko$^2$

Moscow University Physics Bulletin 2015. 70. N 3. P. 190

The neutrino method for monitoring the operating modes of nuclear reactors was proposed and tested in the 1980s–1990s at the Kurchatov Institute. Recent progress in the experimental techniques for antineutrino detection has enabled the development of projects that are focused on the introduction of tech niques that are used in fundamental research in the nuclearpower industry. We report on the current status of the development of a test prototype of the iDREAM (industrial Detector for REactor Antineutrino Monitoring) detector. The detector is a scintillation spectrometer that is based on a liquid organic scintillator with a sensitive volume of 1 m$^3$ and is constructed with due regard for the current experience in the design of the most extensively studied detectors of reactor antineutrinos of this type.

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Optics and spectroscopy. Laser physics

## The effect of an absorbed layer on the resonant frequencies and Q-Factors of spherical microresonators

### Y. A. Demchenko, M. L. Gorodetsky

Moscow University Physics Bulletin 2015. 70. N 3. P. 195

We investigate two approaches to the calculation of the resonant frequency shift and Q-factor modification in a microresonator due to adsorption of a homogeneous isotropic dielectric layer on its surface. The first approach is based on the analytical solution of the characteristic equation for a spherical microres onator in the approximation of a thin dielectric layer on its surface. The second, more general approach, uses the adiabatic invariant. We demonstrate it to be equivalent to the wellknown perturbationtheory technique and use it for the case of a spherical microresonator. Both approaches yield the same result and confirm the previous data. The obtained complex part of the frequency shift allows one to calculate the variation in the Q-factor of a microresonator with a lossy layer.

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Condensed matter physics

## The stochastic nature of phase transformations in a Pd–Ni alloy after electrolytic hydrogenation

### V.M. Avdyukhina, O.V. Akimova, I.S. Levin, A.A. Peganov

Moscow University Physics Bulletin 2015. 70. N 3. P. 201

The results of an Xray diffractometry study of an initially deformed singlephase Pd–25.2 at % Ni alloy sample that were carried out during 460 hours after electrolytic hydrogenation of the sample are pre sented. Longterm stochastic processes of transformation of the shape of diffraction peaks were found, despite the absence of the hydrogenrich βphase in the sample.

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Physics of Earth, atmosphere, and hydrosphere

## Application of photometry method to some hydrodynamic objectives

### N.I. Shevtsov$^1$, E.V. Stepanova$^2$

Moscow University Physics Bulletin 2015. 70. N 3. P. 208

Presented paper contains the results of applying the photometry method to the flow pattern images obtained in the experimental investigation of three different hydrodynamic processes. Characteristic parameters of the currents are calculated on the basis of the obtained data. Comparison of the methods proposed by the authors, with the available software products is held.

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## A nonlinear model of sea surface waves

### K.V. Pokazeev$^1$, A.S. Zapevalov$^2$, V.V. Pustovoytenko$^2$

Moscow University Physics Bulletin 2015. 70. N 3. P. 213

An analytical model that describes the profile of a nonlinear wave on the sea surface was built. The model parameters were calculated on the basis of the statistical characteristics of the wave field that were obtained from in situ experiments. The model takes the group structure of surface waves and the skewness of the distribution of waveinduced elevations of the surface into account. A Jacobi elliptic function of the second kind was used for describing the envelope of a group of waves and the carrier wave.

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